A satellite is revolving round the earth in an orbit of radius r with time period T. If the satellite is revolving round the earth in an orbit of radius r + Δr(Δr << r) with time period T + ΔT(ΔT << T) then.

$\frac{\Delta T}{T}=\frac{3}{2} \frac{\Delta r}{r}$

Since, $T^2=kr^3$

$\Rightarrow 2 \frac{\Delta T}{T}=3 \frac{\Delta r}{r}$

$\Rightarrow \frac{\Delta T}{T}=\frac{3}{2} \frac{\Delta r}{r}$